In some matrix computations for graph objects the adjacency matrix
of the graph is transformed into an ``edge matrix''. Briefly,
if \(E\) is the adjacency matrix of the
graph, the edge matrix is \(A = sign(E+I)^T=[a_{ij}]\).
Thus, \(A\) has ones along the diagonal
and if the graph has no edge between nodes \(i\) and \(j\) the entries
\(a_{i,j}\) and \(a_{j,i}\) are both zero.
If there is an arrow from \(j\) to \(i\)
\(a_{i,j}=1\) and \(a_{j,i} = 0\). If there is an undirected edge, both
\(a_{i,j}=a_{j,i}=1\).